Russian forces were trying to block a city in eastern Ukraine, the region's governor said on Saturday, after a relentless assault on a neighbouring city forced Ukrainian troops to begin withdrawing after weeks of intense fighting.

Russia also launched missile attacks on areas far from the heart of the eastern battles. Serhiy Haidai, governor of Luhansk province, said on Facebook that Russian and separatist fighters tried to blockade the city of Lysychansk from the south.

The city lies next to Sievierodonetsk, which has endured relentless assault and house-to-house fighting for weeks.

Russia's Interfax news agency quoted a spokesman for the separatist forces, Andrei Marochko, as saying Russian troops and separatist fighters had entered Lysychansk and that fighting was taking place in the heart of the city.

There was no immediate comment on the claim from the Ukrainian side.

Lysychansk and Sievierodonetsk have been the focal point of a Russian offensive aimed at capturing all of eastern Ukraine's Donbas region and destroying the Ukrainian military defending it — the most capable and battle-hardened segment of the country's armed forces.

The two cities and surrounding areas are the last major pockets of Ukrainian resistance in Luhansk, 95 per cent of which is under Russian and local separatist control.

The Russians and separatists also control about half of Donetsk, the second province in the Donbas. Russian bombardment has reduced most of Sievierodonetsk to rubble and cut its population from 100,000 to 10,000.

Some Ukrainian troops are holed up in the huge Azot chemical factory on the city's edge, along with about 500 civilians. A separatist representative, Ivan Filiponenko, said forces evacuated 800 civilians from the plant during the night, Interfax reported.

After Haidai said on Friday that Ukrainian forces had begun retreating from Sievierodonetsk, military analyst Oleg Zhdanov said some of the troops were heading for Lysychansk. But Russian moves to cut off Lysychansk will give those retreating troops little respite.

Some 1,000 kilometres to the west, four Russian rockets hit a “military object” in Yaroviv, Lviv regional governor Maksym Kozytskyy said.

He did not give further details of the target, but Yaroviv has a sizable military base used for training fighters, including foreigners who have volunteered to fight for Ukraine.

Russian rockets struck the Yaroviv base in March, killing 35 people. The Lviv region, although far from the front lines, has come under fire at various points in the the war as Russia's military worked to destroy fuel storage sites.

About 30 Russian rockets also were fired on the Zhytomyr region in central Ukraine on Saturday morning, killing one Ukrainian soldier, regional governor Vitaliy Buchenko said.

In the north, about 20 rockets were fired from Belarus into the Chernihiv region, the Ukrainian military said.

Ukraine's air command said Russian long-range Tu-22 bombers were deployed from Belarus for the first time. The neighbouring country hosts Russian military units and was used as a staging ground before Russia invaded Ukraine, but its own troops have not crossed the border.

Russian President Vladimir Putin and Belarusian President Alexander Lukashenko were to meet on Saturday in St. Petersburg.

A senior US defence official, speaking in Washington on condition of anonymity, on Friday called the Ukrainians' move out of Sievierodonetsk a “tactical retrograde” to consolidate forces into positions where they can better defend themselves.

This will add to Ukraine's effort to keep Russian forces pinned down longer in a small area, the official said.

Following a botched attempt to capture Kyiv, Ukraine's capital, in the early stage of the invasion that started on February 24, Russian forces have shifted their focus to the Donbas, where the Ukrainian forces have fought Moscow-backed separatists since 2014.

After repeated Ukrainian requests to its Western allies for heavier weaponry to counter Russia's edge in firepower, four medium-range American rocket launchers arrived this week, with four more on the way.

The senior US defence official said on Friday that more Ukrainian forces are training outside Ukraine to use the High Mobility Artillery Rocket Systems (HIMARS) and are expected back in their country with the weapons by mid-July.

The rockets can travel about 70 kilometres. Also to be sent are 18 US coastal and river patrol boats.

The official said there is no evidence Russia has intercepted any of the steady flow of weapons into Ukraine from the US and other nations. Russia has repeatedly threatened to strike, or actually claimed to have hit, such shipments.